Diagnostic and control systems and methods for substrate processing systems using DC self-bias voltage

ABSTRACT

A substrate processing system includes a processing chamber including a showerhead, a plasma power source and a pedestal spaced from the showerhead to support a substrate. A filter is connected between the showerhead and the pedestal. A variable bleed current circuit is connected between the filter and the pedestal to vary a bleed current. A controller is configured to adjust a value of the bleed current and configured to perform curve fitting based on the bleed current and DC self-bias voltage to estimate at least one of electrode area ratio, Bohm current, and radio frequency (RF) voltage at a powered electrode.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present disclosure is a divisional of U.S. patent application Ser.No. 13/912,256 filed on Jun. 6, 2013. This application claims thebenefit of U.S. Provisional Application No. 61/715,630, filed on Oct.18, 2012 and U.S. Provisional Application No. 61/657,331, filed Jun. 8,2012. The entire disclosures of the applications referenced above areincorporated herein by reference.

FIELD

The present disclosure relates to substrate processing systems and moreparticularly to diagnostic and control systems and methods for substrateprocessing systems using DC self-bias voltage.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Substrate processing tools are used to deposit material on a substrateand/or to etch material from the substrate. For example, the substratemay include a semiconductor wafer. Some substrate processing toolsgenerate plasma during operation. Examples include plasma enhancedchemical vapor deposition (PECVD) systems, plasma enhanced atomic layerdeposition (PEALD) systems, etc. Plasma may be generated in thesesystems using capacitively coupled plasma (CCP).

Most of the systems using CCP offer a very limited number of plasmadiagnostic measurements (such as pressure, system voltages, currents,etc.) which can be used to adjust setpoint operating parameters aschamber pressure, gas flow and RF power. Furthermore, pressure, gas flowand RF power signals may not give complete characterization of thesystem. Such an incomplete characterization can lead to process drift.Additional system metrics are often needed for adequate system control.

SUMMARY

A substrate processing system includes a processing chamber including ashowerhead, a plasma power source and a pedestal spaced from theshowerhead to support a substrate. A filter is connected between theshowerhead and the pedestal. A variable bleed current circuit isconnected between the filter and the pedestal to vary a bleed current. Acontroller is configured to adjust a value of the bleed current andconfigured to perform curve fitting based on the bleed current and DCself-bias voltage to estimate at least one of electrode area ratio, Bohmcurrent, and radio frequency (RF) voltage at a powered electrode.

In other features, the variable bleed current circuit comprises avariable resistor circuit. The controller is configured to vary aresistance of the variable resistor circuit to N values and to record Npairs of the bleed current and the DC self-bias voltage, wherein N is aninteger greater than one. The controller is configured to perform thecurve fitting based on the N values of the bleed current and the DCself-bias voltage.

In other features, the variable bleed current circuit comprises avariable current source. The controller is configured to vary currentsupplied by the variable current source to N values and to record Npairs of the bleed current and the DC self-bias voltage, wherein N is aninteger greater than one. The controller is configured to perform thecurve fitting based on the N values of the bleed current and the DCself-bias voltage.

In other features, the substrate processing system performs depositionand the controller is configured to adjust a deposition operatingparameter of the substrate processing system based on the at least oneof the electrode area ratio, the Bohm current, and the radio frequency(RF) voltage at the powered electrode.

In other features, the controller is configured to perform diagnosticson the substrate processing system based on the at least one of theelectrode area ratio, the Bohm current, and the radio frequency (RF)voltage at the powered electrode. The filter is configured to blockradio frequency signals and to pass DC signals. The substrate processingsystem generates plasma using capacitive coupling. The plasma powersource is coupled to the showerhead and wherein the pedestal isconnected to ground.

In other features, a current sensor senses bleed current flowing throughthe variable resistor circuit. The controller is configured to estimatethe Bohm current and to estimate plasma density from the Bohm current.The controller is configured to adjust a deposition operating parameterof the substrate processing system based on the plasma density.

A substrate processing system includes a processing chamber including ashowerhead, a plasma power source and a pedestal spaced from theshowerhead to support a substrate. The plasma power source suppliesfirst radio frequency (RF) power to create plasma between the showerheadand the substrate. An RF power source is coupled by the first capacitorto the probe to supply second RF power. A controller is configured toestimate film thickness based on the second RF power and DC self-biasvoltage.

In other features, the substrate processing system is configured todeposit film on the substrate and the controller is configured to alteran operating parameter of the substrate processing system based on thefilm thickness. The substrate processing system is configured to depositfilm on the substrate. The controller is configured to determine a rateof change in the film thickness. The controller is configured to alteran operating parameter of the substrate processing system based on therate of change of the film thickness.

In other features, the substrate processing system generates the plasmausing capacitive coupling. The plasma power source is coupled to theshowerhead. The pedestal is connected to ground. The second RF power isless than the first RF power.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description, the claims and the drawings. Thedetailed description and specific examples are intended for purposes ofillustration only and are not intended to limit the scope of thedisclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of an example of a PECVD system;

FIG. 2A is an electrical schematic of example of a capacitively coupledplasma (CCP) circuit according to the present disclosure;

FIG. 2B is an electrical schematic and functional block diagram ofexample of CCP circuit and controller according to the presentdisclosure;

FIG. 3 illustrates an example of a method for operating the controllerof FIG. 2B;

FIGS. 4 and 5 are electrical schematics of a circuit representing thesubstrate processing system;

FIG. 6 illustrates time varying sheath voltages and currents;

FIG. 7A illustrates the circuit of FIG. 4 with a variable bleed resistorcircuit and current sensor circuit;

FIG. 7B illustrates an example of the variable bleed resistor circuit;

FIG. 7C illustrates the circuit of FIG. 4 with a variable current sourceand current sensor circuit;

FIG. 8 illustrates DC self-bias voltage as a function of bleed current;

FIG. 9 illustrates DC self-bias voltage as a function of RF voltage;

FIG. 10 illustrates DC self-bias voltage as a function of time;

FIG. 11 is a functional block diagram of a controller that estimateselectrode area ratio, Bohm current and RF voltage at the poweredelectrode based on the DC self-bias voltage and bleed current; and

FIG. 12 is a flowchart illustrating an example of a method performed bythe controller of FIG. 11.

DETAILED DESCRIPTION

The present disclosure describes the use of DC self-bias voltage insubstrate processing systems using capacitively coupled plasma (CCP).The present disclosure monitors changes in DC self-bias voltage and/orbleed current to estimate other system parameters, for diagnosticpurposes and/or for control of the substrate processing system.

Referring now to FIG. 1, an example of a semiconductor processing system100 is shown and includes a process chamber 102. While a typical PECVDsystem is shown for illustration purposes, other substrate processingsystems may be used. The semiconductor processing system 100 furtherincludes a showerhead 110 to deliver process gases to the processchamber 102. A plasma power source 120 provides RF power to theshowerhead 110 to create plasma. A pedestal 134 may be connected to areference potential such as ground. Alternatively an electrostatic chuck(ESC) may be used in substitute for a pedestal (not common). The RFsignals supplied by the plasma power source 120 have a power and afrequency sufficient to generate plasma from one or more process gases.In some examples, the plasma power source 120 may be connected to thepedestal 134 instead of the showerhead 110 and the showerhead 110 may beconnected to ground.

The pedestal 134 may include a chuck, a fork, or lift pins (all notshown) to hold and transfer a substrate 136 during and betweendeposition and/or plasma treatment reactions. The chuck may be anelectrostatic chuck, a mechanical chuck or various other types of chuck.

The process gases are introduced to the showerhead 110 via inlet 142.Multiple process gas lines are connected to a manifold 150. The processgases may be premixed or not. Appropriate valves and mass flowcontrollers (generally identified at 144-1, 144-2, and 144-3) areemployed to ensure that the correct gases and flow rates are used duringsubstrate processing. Process gases exit the process chamber 102 via anoutlet 160. A vacuum pump 164 typically draws process gases out of theprocess chamber 102 and maintains a suitably low pressure within thereactor by a flow restriction device, such as a valve 166. A controller168 may sense operating parameters such as chamber pressure andtemperature inside the processing chamber using sensors 170 and 172. Thecontroller 168 may control the valves and mass flow controllers 144-1,144-2 and 144-3. The controller 168 may also control the plasma powersource 120.

Measurement of Film Thickness

Referring now to FIG. 2A, measurement of film growth may be performed asfollows. Plasma is sustained by an RF generating source coupled to theplasma through a capacitor C_(B1). For this discussion it is assumedthat plasma exists only between the system electrodes and not between apowered electrode and the chamber walls (i.e. it is assumed there is noparasitic plasma). A probe 180 is introduced into the plasma. The probe180 is driven by a second continuous RF source (RF₂) coupled to theprobe 180 through a blocking capacitor C_(B2) as shown in FIG. 2A. Forthis configuration, RF source RF₁ provides a first RF power level tosustain the plasma and is controlled using feedback to a given RF powerset point. The second RF source RF₂ provides a second RF power level asis needed to provide a desired RF voltage at the terminals of theblocking capacitor C_(B2). The RF signals from RF source RF₁ arecontinuous signals rather than pulsed RF signals. The second RF powerlevel is less than the first RF power level. The second RF source RF₂has a minimal perturbative effect on the plasma.

Application of RF energy to a plasma through a coupling (blocking)capacitor typically results in a DC self-bias voltage across thatcapacitor. A discussion of how this voltage is formed is given in Y. P.Song et. al., J Phys. D. Appl. Ph., V23 (1990), p. 673-681, which ishereby incorporated by reference in its entirety. The approach detailedin Song et. al. focuses on the current flows in the system and employesthe fact that the time averaged DC currents through the system mustequal zero. As such it may be described as a “current centric” approach.An alternative discussion of DC self-bias is given by K. Kohler et. al.,J. Appl. Phys. 57 (1), January 1985 p. 58-66 which is herebyincorporated by reference in its entirety. This second approach notesthat in the high electron mobility in all such systems forces the plasmapotential to always achieve the highest positive potential in the systemso that electron flow to walls or other surfaces is sufficiently low asto permit an equilibrium steady state condition. This results in severalvoltage conditions that must be satisfied if an equilibrium state is tooccur. As such this approach may be described as a “voltage centric”approach. Thus a DC self-bias voltage is developed across the blockingcapacitor C_(B2). If no deposited film is present (i.e. C_(film)=∞),then the measured DC self-bias voltage is the same as the DC self-biasvoltage that would be measured on the surface of the probe 180 incontact with plasma. However if a film is deposited, there will be anadditional capacitance added to this system in the form of C_(film). Forthis case, the DC self-bias voltage of the surface in contact with theplasma does not change, but the measured DC self-bias voltage willchange as a result of DC voltage division between C_(film) and theblocking capacitor C_(B2). This situation can be described by theequations below:

$\begin{matrix}{C_{film} = \frac{ɛ_{o}ɛ_{r}A_{f}}{d}} & (1) \\{V_{{meas}\;\_\; D\; C} = {{V_{{True}\;\_\; D\; C}\frac{C_{Film}}{C_{Film} + C_{B\; 2}}} = {V_{{True}\;\_\; D\; C}\frac{ɛ_{o}ɛ_{r}A_{f}}{{ɛ_{o}ɛ_{r}A_{f}} + {C_{B\; 2}d}}}}} & (2) \\{{V_{{True}\;\_\; D\; C} = {{V_{{RF}\; 2}\frac{C_{p\; s} - C_{gs}}{C_{p\; s} + C_{gs}}} = {V_{{RF}\; 2}\kappa}}};} & (3) \\{d = {\frac{ɛ_{o}ɛ_{r}A_{f}}{C_{B\; 2}}{\left( {\frac{V_{{RF}\; 2}\kappa}{V_{{meas}\;\_\; D\; C}} - 1} \right).}}} & (4)\end{matrix}$where A_(f) is the area of the electrode, d is the thickness of thefilm. From these equations, the change in the measured DC self-biasvoltage will yield a measure of the deposited film capacitance. If therelative permittivity of this capacitance is known, the thickness of thedeposited film can be determined.

In FIG. 2B, a controller 200 includes a film thickness estimating module204 and an operating parameter adjustment module 208. The controller 200receives the measured DC voltage and the RF voltage V_(RF2). The filmthickness estimating module 204 estimates the film thickness based onthe relationship set forth above. The operating parameter adjustmentmodule 208 adjusts an operating parameter of the substrate processingsystem based on the film thickness and/or changes in the film thicknessas a function of time.

In FIG. 3, an example of a method for operating the controller of FIG.2B is shown. At 222, V_(RF2) is applied in the circuit of FIG. 2A and at224 V_(RF2) is measured. At 226, the DC self-bias voltage V_(meas) _(_)_(DC) is measured. At 228, the thickness of the film is calculated. At230, one or more operating parameters of the substrate processing systemare altered based on the film thickness and/or changes in the filmthickness as a function of time.

Estimating Electrode Area Ratio, Bohm Current, and/or RF Voltage at thePowered Electrode

The discussion of Y. P. Song et. al., J Phys. D. Appl. Ph., V23 (1990),p. 673-681 does not included analysis of the effect of a DC (only—no RF)current drawn from the RF powered electrode (be it either the showerheador pedestal). This may be done by introducing an RF filter to prevent RFcurrent from being drawn. However, the ideas presented by Y. P. Song et.al., J Phys. D. Appl. Ph., V23 (1990), p. 673-681 can be adapted to forman analysis that gives the DC self-bias voltage response to a DC currentdrawn (or “bled”) from a powered electrode. As will be discussed below,this relationship between the bleed current and DC self-bias voltage canbe used to predict DC self-bias voltage change in terms of electrodeareas and Bohm current density to each electrode. In the followinganalysis, a current based approach will be used as discussed by Y. P.Song et. al. In the current based approach, the DC current averaged overan RF cycle must equal zero. This is the same as imposing the conditionthat no net DC current can flow through this system because of thepresence of the blocking capacitor (C_(b) in FIG. 7A). Using thiscondition, an expression for the DC self-bias voltage is derived.

As will be described more fully below, a resistance of a variable bleedresistor R_(V) is adjusted to vary a bleed current i_(R). For each valueof the bleed resistor, the DC self-bias voltage and the bleed currentvalues are recorded. Curve fitting is performed based on the pairs ofvalues and a relationship (derived below) to estimate values for theeffective electrode area ratio

$\frac{A_{b}}{A_{a}},$Bohm current i_(B) and RF voltage at the electrode.

The Bohm current density J_(B) (derived as i_(B) divided by theelectrode area) may also be used to estimate plasma density, which canbe used as a feedback parameter to control an operating parameter of thesubstrate processing system and/or for diagnostic purposes. Likewise,the effective electrode area ratio and the RF voltage may be used fordiagnostic purposes and/or as a feedback parameter to control anoperating parameter of the substrate processing system. Changes in theeffective electrode area ratios can signal hardware failures, presenceof excessive parasitic plasma or an unwanted coating on the innersurface of the plasma chamber.

Referring now to FIGS. 4 and 5, circuit models are shown. In FIG. 4, acircuit 300 is shown to include an RF source 304 that is connected by acapacitor C_(b) to a showerhead 308. For example only, the RF source 304provides a signal V_(RF)(t)=V_(RF) sin (ωt). Plasma 312 is createdbetween the showerhead 308 and a pedestal 316. First and second sheathareas A_(a) and A_(b) are created with corresponding sheath voltagesV_(a)(t) and V_(b)(t). An RF filter 322 is connected to the showerhead308 and to a current source 326, which sources or sinks current i_(R).The RF filter 322 is used to block RF signals and pass DC signals.

In FIG. 5, an equivalent schematic that simulates plasma is shown toinclude capacitors C_(a) and C_(b) connected in series, current sourcesI_(a0) and I_(b0) connected in series, and diodes 330 and 332 connectedin series.

For a current based approach, several conditions must be satisfied.Current over an RF cycle to an electrode averages to zero if the bleedcurrent is zero. If the bleed current is non-zero, the current over anRF cycle averages to the bleed current.

Referring now to FIG. 6, time varying sheath voltages and currents areshown as a function of time. The following equations illustraterelationships between t₁ and t₂ and t_(a) and t_(b):

$\begin{matrix}{{{\frac{2\pi}{\omega} = T};}{{{\frac{T}{4} - t_{1}} = {t_{2} - \frac{T}{4}}},{therefore}}{{t_{2} = {\frac{\pi}{\omega} - t_{1}}};}} & (5) \\{{{{t_{a} + t_{b}} = \frac{2\pi}{\omega}};}{and}} & (6) \\{{t_{2} - t_{1}} = {t_{a}.}} & (7)\end{matrix}$

Based on (5) and (6), the current balance relationship can be writtenas:

${{t_{a}J_{Bb}A_{b}} - {t_{b}J_{Ba}A_{a}}} = {{i_{R}\left( {t_{a} + t_{b}} \right)} = {\frac{2\pi}{\omega}i_{R}}}$where J_(Ba) and J_(Bb) are Bohm current densities at sheaths a and b,respectively. Using equation (6), the current balance relationship canbe rewritten as:

${{\frac{2\pi}{\omega}i_{R}} = {{t_{a}J_{Bb}A_{b}} - {\left( {\frac{2\pi}{\omega} - t_{a}} \right)J_{Ba}A_{a}}}};$${i_{R} = {{\frac{t_{a}\omega}{2\pi}\left( {{J_{Bb}A_{b}} + {J_{Ba}A_{a}}} \right)} - {J_{Ba}A_{a}}}};$$t_{a} = {\frac{2\pi}{\omega}\left\lbrack \frac{i_{R} + {J_{Ba}A_{a}}}{{J_{Bb}A_{b}} + {J_{Ba}A_{a}}} \right\rbrack}$

There is a relationship between the voltage at t₁ or V(t₁) and thevoltages V_(DC) _(_) _(bias) and V_(RF). The floating potential isassumed to be relatively small. Therefore:V _(b)(t ₁)≈0=V _(RF) sin(ωt ₁)−V _(DC) _(_) _(bias);V _(DC) _(_) _(bias) =V _(RF) sin(ωt ₁);  (8):

Using the relationship between t_(a) and t₁:

$\begin{matrix}{{{\left. \begin{matrix}{t_{a} = {t_{2} - t_{1}}} \\{t_{2} = {\frac{\pi}{\omega} - t_{1}}}\end{matrix} \right\} t_{a}} = {{t_{2} - t_{1}} = {{\left( {\frac{\pi}{\omega} - t_{1}} \right) - t_{1}} = {\frac{\pi}{\omega} - {2t_{1}}}}}};} & (9)\end{matrix}$Inserting (7) and (8) into (9) yields:

${{\frac{2\pi}{\omega}\left\lbrack \frac{i_{R} + {J_{Ba}A_{a}}}{{J_{Bb}A_{b}} + {J_{Ba}A_{a}}} \right\rbrack} = {\frac{\pi}{\omega} - {\frac{2}{\omega}{\sin^{- 1}\left( \frac{V_{D\; C\;\_\;{bias}}}{V_{RF}} \right)}}}},$which can be rearranged as:

$\begin{matrix}{{{\frac{V_{D\; C\;\_\;{bias}}}{V_{RF}} = {\sin\left\{ {\frac{\pi}{2}\left( {1 - {2\left\lbrack \frac{i_{R} + {J_{Ba}A_{a}}}{{J_{Bb}A_{b}} + {J_{Ba}A_{a}}} \right\rbrack}} \right)} \right\}}};}{{or}\mspace{14mu}{as}}{\frac{V_{D\; C\;\_\;{bias}}}{V_{RF}} = {\cos\left( {\pi\left\lbrack \frac{i_{R} + {J_{Ba}A_{a}}}{{J_{Bb}A_{b}} + {J_{Ba}A_{a}}} \right\rbrack} \right)}}} & (10)\end{matrix}$

Assuming that the plasma has an electron temperature T_(e) and that thesheath edge plasma densities are the same at both sheath edges, the Bohmcurrent densities are the same at each sheath, or J_(Ba)=J_(Bb)=J_(B).As a result, equation (10) can be rewritten as follows:

$\begin{matrix}{{{\frac{V_{D\; C\;\_\;{bias}}}{V_{RF}} = {\cos\left( {\pi\left\lbrack \frac{i_{R} + {J_{B}A_{a}}}{{J_{B}A_{b}} + {J_{B}A_{a}}} \right\rbrack} \right)}};}{{\frac{V_{D\; C\;\_\;{bias}}}{V_{RF}} = {\cos\left( {\pi\left\lbrack \frac{\frac{i_{R}}{J_{B}A_{a}} + 1}{\frac{A_{b}}{A_{a}} + 1} \right\rbrack} \right)}};}{or}{\frac{V_{D\; C\;\_\;{bias}}}{V_{RF}} = {\cos\left( {\pi\left\lbrack \frac{\frac{i_{R}}{i_{B}} + 1}{\frac{A_{b}}{A_{a}} + 1} \right\rbrack} \right)}}{where}{i_{B} = {J_{B}A_{a}}}} & (11)\end{matrix}$

As can be seen in equation (11),

$\frac{V_{D\; C\;\_\;{bias}}}{V_{RF}}$depends on the ratio of the total bleed current i_(R) to the total Bohmcurrent i_(B) (or Bohm current density times the electrode areaJ_(B)A_(b)) and on the electrode area ratio

$\frac{A_{b}}{A_{a}}.$For small values of bleed current i_(R) and

${\frac{A_{b}}{A_{a}} \approx 1},$the ratio of

$\frac{V_{D\; C\;\_\;{bias}}}{V_{RF}}$varies nearly linearly with bleed current i_(R). For

${\frac{A_{b}}{A_{a}} \approx 1},$the ratio of

$\frac{V_{D\; C\;\_\;{bias}}}{V_{RF}}$departs from linearity as bleed current i_(R) becomes a significantfraction of the Bohm current i_(B).

Referring now to FIG. 7A, the circuit 300 of FIG. 4 is shown to includea variable bleed current circuit 350 to vary the bleed current. Forexample only, the variable bleed current circuit 350 may include avariable resistor circuit R_(V). A resistance value of the variableresistor circuit R_(V) may be varied to adjust the bleed current. Acurrent sensor circuit 352 senses the bleed current. A voltage sensorcircuit 354 senses the DC self-bias voltage. A switch 358 may be used toconnect and disconnect the variable bleed current circuit 350. Thevoltage sensor circuit 354 preferably has a high impedance. In someexamples, the impedance of the voltage sensor circuit 354 is greaterthan 10 MΩ. The current sensor circuit 352 preferably has zero impedanceor a very low impedance.

In one example, plasma was generated using nitrogen N₂ at a pressure of2.5 Torr and RF power of 200 Watts at 13.56 MHz. Work was done at 2.5Torr because the plasma was observed to be well localized to theelectrodes. This lack of plasma spreading provided a constant effectiveelectrode area ratio and allowed geometric estimation of the effectiveelectrode area ratio. A DC power supply was connected to the showerheadvia a filter, which provided 35 dB attenuation at 13.56 MHz. Bleedcurrent i_(R) and DC self-bias voltage pairs were measured usingmultiple different bleed resistor values set by a variable bleedresistor R_(V).

In FIG. 7B, an example of a variable bleed resistor R_(V) is shown toinclude series connected pairs of resistors R₁, R₂, . . . and R_(T) andswitches S₁, S₂, . . . and S_(T), respectively, that are connected inparallel, where T is an integer greater than one. The switches S₁, S₂, .. . and S_(T) can be opened or closed to provide different resistancevalues. This would allow variation in the amount of current bled fromthe showerhead. As can be appreciated, other arrangements andcombinations of switches and resistors can be used.

In FIG. 7C, the variable bleed current circuit 350 is shown to include avariable current source 362 to vary the bleed current.

Referring now to FIG. 8, the DC self-bias voltage V_(DC) _(_) _(bias) isshown relative to the bleed current i_(R). In this illustrative example,the experimental area ratio

$\left( {\frac{A_{b}}{A_{a}} = \frac{C_{ped}}{C_{shrhd}}} \right)$was 0.825 and the amplitude of the applied RF voltage V_(RF) was 220 V.As can be seen, the model data fits with the experimental results. Themodel departs from linearly as the magnitude of the bleed current i_(R)increases. The experimental electrode area ratio

$\frac{A_{b}}{A_{a}}$was 0.825 and the model-fit electrode area ratio

$\frac{A_{b}}{A_{a}}$was 0.899. The expected Bohm current i_(B) was 90.70 mA and themodel-fit Bohm current i_(B) was 94.464 mA. These values for i_(B) maydivided by the electrode area A_(b) (if known) to obtain thecorresponding Bohm current density values J_(B).

By fitting the model to the DC self-bias voltage V_(DC) _(_) _(bias) andbleed current i_(R), the electrode area ratio

$\frac{A_{b}}{A_{a}},$total Bohm current J_(B) received by powered electrode, and the RFvoltage at the powered electrode V_(RF) can be determined. The RFvoltage at the powered electrode V_(RF) can also be measured using anoscilloscope. If the RF voltage at the powered electrode V_(RF) ismeasured, the model reduces to two unknowns.

The model does not require knowledge of plasma density or electrontemperature. If the electron temperature T_(e), the electrode area A_(b)and the atomic mass of the ion species is known, a Bohm argument can beused to determine plasma density from the fitted Bohm current i_(B). Adifferential bias resistance can also be derived by differentiatingequation (11) with respect to bleed current i_(R).

Referring now to FIG. 9, the area ratio can alternatively be determinedfrom Köhler, et. al., J. Appl. Phys. 57 (1), January 1985 using avoltage-centric model. Using a voltage-based approach, the RF and DCvoltage conditions that must be satisfied over an RF cycle aredetermined and then an expression for DC self-bias voltage is derived.

${V_{D\; C\;\_\;{bias}} = {V_{RF}\left( \frac{C_{pwrd} - C_{grd}}{C_{pwrd} + C_{grd}} \right)}};$or$\frac{C_{pwrd}}{C_{grd}} = \left( \frac{1 + \frac{V_{D\; C\;\_\;{bias}}}{V_{RF}}}{1 - \frac{V_{D\; C\;\_\;{bias}}}{V_{RF}}} \right)$

The voltage-based approach also provides good results as well. Thefitted slope was −0.204. The experimental area ratio

$\left( {\frac{A_{b}}{A_{a}} = \frac{C_{ped}}{C_{shrhd}}} \right)$was 0.815. The implied area ratio

$\left( {\frac{A_{b}}{A_{a}} = \frac{C_{ped}}{C_{shrhd}}} \right)$was 0.825. The model fit area ratio

$\left( {\frac{A_{b}}{A_{a}} = \frac{C_{ped}}{C_{shrhd}}} \right)$was 0.899.

With a few additional assumptions (electron temperature T_(e), electrodearea A and mass of the ion species (M_(i))), the plasma density can alsobe estimated from the Bohm current using the relationship set forthbelow:

$n = \frac{i_{B}}{A\sqrt{\frac{{kT}_{e}}{M_{i}}}}$where n is the plasma density, A is the electrode area, M_(i) is themass of the ion species in the plasma, k is Bolzman's constant and T_(e)is the electron temperature (in units of eV). The plasma density can beused to vary an operating parameter of the substrate processing system.

In another example, the time dependent characteristics of the DCself-bias voltage are monitored as the variable resistor R_(V) isswitched into or out of the circuit or removed entirely from thecircuit. For example only, a first value of R_(V) is used to bleedcurrent to ground. This will cause a shift in the DC self-bias voltagein accordance with the equations given above. Then, the resistor isremoved from the circuit by opening the circuit. At this point, no bleedcurrent is drawn and the DC self-bias voltage will transition over abrief period of time to a value corresponding to no bleed current asindicated in the equations given above. An example of this behavior isillustrated in FIG. 10.

Alternatively the variable resistor R_(V) can switch from one resistancevalue to another resistance value and then the change in DC self-biasbehavior can be monitored over time. The behavior of the DC self-biasvoltage during the recovery time shows a characteristic shape andrecovery time similar to (but not the same as) that seen for an RCcircuit. There will be a charging of the blocking capacitance but thecharging current is mediated by the Bohm sheath mechanism. For example,an expression of the form below can be fit to the recovery of the DCbias voltage:

${V_{D\; C\;\_\;{bias}}(t)} = {A + {B\mspace{11mu}\exp\left\{ {- \frac{\left( {t - t_{o}} \right)}{\tau}} \right\}}}$where τ is a time constant and t₀ is the onset of the voltage change.Tracking of changes in τ provides a parameter by which changes in thesystem can be detected.

Referring now to FIG. 11, an example of a controller 400 is shown toinclude a resistance selecting module 402, a curve fitting module 404, adiagnostic module 420 and an operating parameter adjustment module 422.The curve fitting module 404 performs curve fitting based on the bleedcurrent and DC self-bias voltage pairs for different values of thevariable bleed resistor R_(V). The curve fitting module 404 includes anelectrode area ratio estimating module 406 to estimate the electrodearea ratio, a Bohm current estimating module 410 to estimate the Bohmcurrent and an RF voltage (at the powered electrode) estimating module412 to estimate the RF voltage at the powered electrode.

Referring now to FIG. 12, an example of a method 500 for operating thecontroller is shown. The method includes setting a value of the variablebleed resistor R_(V) to a first value at 506. At 510, the DC self-biasvoltage and the bleed current I_(R) are stored. At 512, a value of thevariable bleed resistor R_(V) is adjusted and the DC self-bias voltageand the bleed current I_(R) are stored at 520. At 524, the controllerdetermines whether there are sufficient samples. If false, controlreturns to 512. When 524 is true, the controller uses curve fitting todetermine the electrode area ratio, the Bohm current and/or the RFvoltage at the powered electrode based on the relationship set forthabove at 530. At 534, control optionally uses the Bohm current to alteran operating parameter of the substrate processing system. At 540,control optionally uses the electrode area ratio or the RF voltage atthe powered electrode for diagnosis purposes.

In this application, including the definitions below, the termcontroller or module may be replaced with the term circuit. The termmodule may refer to, be part of, or include an Application SpecificIntegrated Circuit (ASIC); a digital, analog, or mixed analog/digitaldiscrete circuit; a digital, analog, or mixed analog/digital integratedcircuit; a combinational logic circuit; a field programmable gate array(FPGA); a processor (shared, dedicated, or group) that executes code;memory (shared, dedicated, or group) that stores code executed by aprocessor; other suitable hardware components that provide the describedfunctionality; or a combination of some or all of the above, such as ina system-on-chip.

The term code, as used above, may include software, firmware, and/ormicrocode, and may refer to programs, routines, functions, classes,and/or objects. The term shared processor encompasses a single processorthat executes some or all code from multiple modules. The term groupprocessor encompasses a processor that, in combination with additionalprocessors, executes some or all code from one or more modules. The termshared memory encompasses a single memory that stores some or all codefrom multiple modules. The term group memory encompasses a memory that,in combination with additional memories, stores some or all code fromone or more modules. The term memory may be a subset of the termcomputer-readable medium. The term computer-readable medium does notencompass transitory electrical and electromagnetic signals propagatingthrough a medium, and may therefore be considered tangible andnon-transitory. Non-limiting examples of a non-transitory tangiblecomputer readable medium include nonvolatile memory, volatile memory,magnetic storage, and optical storage.

The apparatuses and methods described in this application may bepartially or fully implemented by one or more computer programs executedby one or more processors. The computer programs includeprocessor-executable instructions that are stored on at least onenon-transitory tangible computer readable medium. The computer programsmay also include and/or rely on stored data.

The foregoing description is merely illustrative in nature and is in noway intended to limit the disclosure, its application, or uses. Thebroad teachings of the disclosure can be implemented in a variety offorms. Therefore, while this disclosure includes particular examples,the true scope of the disclosure should not be so limited since othermodifications will become apparent upon a study of the drawings, thespecification, and the following claims. For purposes of clarity, thesame reference numbers will be used in the drawings to identify similarelements. As used herein, the phrase of least one of A, B, and C shouldbe construed to mean a logical (A or B or C), using a non-exclusivelogical OR. It should be understood that one or more steps within amethod may be executed in different order (or concurrently) withoutaltering the principles of the present disclosure.

What is claimed is:
 1. A substrate processing system, comprising: aprocessing chamber including a showerhead, a plasma power source and apedestal spaced from the showerhead to support a substrate, wherein theplasma power source supplies first radio frequency (RF) power to createplasma between the showerhead and the substrate; a probe arranged in theplasma; a first capacitor; an RF power source coupled by the firstcapacitor to the probe to supply second RF power; and a controllerconfigured to receive a measurement of a DC self-bias voltage across thefirst capacitor, receive a measurement of the second RF power suppliedby the RF power source, and calculate a film thickness using themeasurements of the second RF power and the DC self-bias voltage acrossthe first capacitor.
 2. The substrate processing system of claim 1,wherein the substrate processing system is configured to deposit film onthe substrate and wherein the controller is configured to alter anoperating parameter of the substrate processing system based on the filmthickness.
 3. The substrate processing system of claim 1, wherein thesubstrate processing system is configured to deposit film on thesubstrate, wherein the controller is configured to determine a rate ofchange in the film thickness, and wherein the controller is configuredto alter an operating parameter of the substrate processing system basedon the rate of change of the film thickness.
 4. The substrate processingsystem of claim 1, wherein the substrate processing system generates theplasma using capacitive coupling.
 5. The substrate processing system ofclaim 4, wherein the plasma power source is coupled to the showerheadand wherein the pedestal is connected to ground.
 6. The substrateprocessing system of claim 1, wherein the second RF power is less thanthe first RF power.
 7. The substrate processing system of claim 1,further comprising a voltage sensor circuit connected between the probeto measure the DC self-bias voltage.